4.2 Heat Engines

Heat engines are marvels of engineering that convert thermal energy into mechanical work. They operate between high and low-temperature reservoirs, using a working substance to harness the power of heat flow. Understanding their components and principles is crucial for grasping thermodynamic concepts.

Efficiency is key in heat engine performance. The Carnot efficiency sets the theoretical maximum, while real-world factors like friction and heat loss reduce actual efficiency. Various cycles, such as Otto and Diesel, offer different approaches to harnessing thermal energy in practical applications.

Heat Engines

Components of heat engines

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• Convert thermal energy (heat) into mechanical energy (work) by operating between a high-temperature reservoir (heat source) and a low-temperature reservoir (heat sink)
• Heat flows from the high-temperature reservoir to the low-temperature reservoir, with some of the heat converted into work during this process
• Working substance undergoes the thermodynamic cycle (gas or steam)
• Heat source provides heat to the working substance
• Heat sink absorbs heat from the working substance
• Mechanical components convert the expansion and contraction of the working substance into useful work
  • Pistons
  • Turbines

Factors in heat engine efficiency

• Efficiency is the ratio of work output to heat input, calculated using the formula $\eta = \frac{W}{Q_H}$
  • $\eta$ represents efficiency
  • $W$ represents work output
  • $Q_H$ represents heat input from the high-temperature reservoir
• Carnot efficiency is the maximum theoretical efficiency of a heat engine operating between two temperatures, calculated using the formula $\eta_{Carnot} = 1 - \frac{T_C}{T_H}$
  • $T_C$ represents the temperature of the cold reservoir (heat sink)
  • $T_H$ represents the temperature of the hot reservoir (heat source)
  • A larger temperature difference between the heat source and heat sink leads to higher efficiency
• Irreversibilities and losses reduce the actual efficiency of heat engines below the Carnot efficiency
  • Friction
  • Heat loss
  • Incomplete combustion

Efficiency calculations for ideal gas engines

• Thermodynamic cycles represent the series of processes that the working substance undergoes in a heat engine, returning to its initial state after completing a cycle
• Otto cycle (constant volume heat addition)
  • Efficiency calculated using the formula $\eta = 1 - \frac{1}{r^{\gamma-1}}$
    • $r$ represents the compression ratio
    • $\gamma$ represents the specific heat ratio of the gas
• Diesel cycle (constant pressure heat addition)
  • Efficiency calculated using the formula $\eta = 1 - \frac{1}{r^{\gamma-1}} \left(\frac{r_c^{\gamma}-1}{\gamma(r_c-1)}\right)$
    • $r$ represents the compression ratio
    • $r_c$ represents the cutoff ratio
    • $\gamma$ represents the specific heat ratio of the gas
• Brayton cycle (constant pressure heat addition and rejection)
  • Efficiency calculated using the formula $\eta = 1 - \frac{1}{r_p^{\frac{\gamma-1}{\gamma}}}$
    • $r_p$ represents the pressure ratio
    • $\gamma$ represents the specific heat ratio of the gas

Thermodynamic principles and analysis

• The first law of thermodynamics relates the change in internal energy of a system to heat added and work done
• Pressure-volume diagrams are used to visualize and analyze thermodynamic cycles
• An isentropic process is an idealized thermodynamic process that is adiabatic and reversible
• The Kelvin-Planck statement of the second law of thermodynamics states that it is impossible to construct a heat engine that operates in a cycle and produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work